Question

arianna opened a savings account and deposited $1,334.00 as principal. the account earns 7% interest, compounded quarterly. what is the balance after 3 years? use the formula $a = p\left(1 + \frac{r}{n}\
ight)^{nt}$, where $a$ is the balance (final amount), $p$ is the principal (starting amount), $r$ is the interest rate expressed as a decimal, $n$ is the number of times per year that the interest is compounded, and $t$ is the time in years. round your answer to the nearest cent.

Explanation:

Step1: Identify given values

$P = 1334.00$, $r = 0.07$, $n = 4$, $t = 3$

Step2: Calculate periodic rate

$\frac{r}{n} = \frac{0.07}{4} = 0.0175$

Step3: Calculate total compound periods

$nt = 4 \times 3 = 12$

Step4: Compute growth factor

$(1 + 0.0175)^{12} \approx 1.2314393$

Step5: Calculate final balance

$A = 1334.00 \times 1.2314393$

Answer:

$1642.74$